Role of interlayer couplings in bilayer Superconductors:A variational Monte Carlo Study

Abstract

The ground state superconducting and magnetic properties of bilayer cuprate superconductors are studied using a t-J model with interlayer couplings using the variational Monte Carlo (VMC) method. As a separate exercise, but relevant to the single layers and ladder compounds, a brief study of an impurity doped Hubbard model via the quantum Monte Carlo method is reported. To settle a crucial question regarding the symmetry of the superconducting order parameter, we investigated the stability of a number of different pairing symmetries for a t-J bilayer. For model parameter values that are suggested by experimental studies on bilayer superconductors, the favourable pairing symmetry of the superconducting state is found to be d-wave. Superconductivity coexists with antiferromagnetic long range order in the underdoped region. Superconducting and magnetic properties in the pure superconducting and the coexisting state are examined and it is convincingly shown that in the coexisting phase, both the antiferromagnetic and superconducting correlations are enhanced. Further, to compliment the phase diagrams of planar systems available in literature, we obtained a ground state phase diagram for a t-J bilayer as a function of interlayer couplings. The phase diagram shows rich features, such as, a crossover of superconducting correlations from being predominantly planar to strongly interplanar as interlayer exchange coupling is increased, a non-monotonic variation of the critical hole concentraion, upto which the d-wave superconducting phase remains stable, as a function of interplanar hopping parameter etc. In addition, there is a lowering of superconducting correlations as a function of interlayer hopping in the under and optimally doped phases, while these are enhanced in the overdoped region for moderate values of the coupling parameter. However the effect of interlayer coupling parameters on magnetic correlations are much less pronounced. Finally, to complete our discussion on bilayered superconductors, we studied the consequence of interlayer pair tunneling using a grand canonical VMC method, where the superconducting state of a bilayer is described by a variational wavefunction that is a product of two Gutzwiller projected d-wave BCS wavefunctions, one for each layer, with variable particle number. Our calculations show that the energy due to the tunneling of Cooper pairs across the layers has interesting bahaviour. However, the magnitude of energy is found to be too small to have any significant effect on the physical properties at least for realistic values of the tunneling parameter...